![]() ![]() In view of these advances, it is important to note that under practical conditions, optical atomic clocks are not exclusively limited by QPN. ![]() The realization of such tailored entangled states on optical clock transitions is a major challenge for experiment 26, 27, 28 and theory 29, 30, 31, 32, 33, 34. Spin squeezed states can be generated with trapped ions 18, 19 and in cold atomic gases 20, 21, 22, and have already been used in proof-of-principle experiments to demonstrate a reduction of quantum projection noise (QPN) in measurements of small phases on microwave transitions 23, 24, 25, 26. In particular, spin squeezed states 14, 15, 16 received much attention due to their practicability and noise resilience 13, 17. Accordingly, approaches from quantum metrology 13 are being pursued which promise to achieve an improvement through the use of entangled atoms. For these applications, high clock stability is vital in order to reach a given frequency uncertainty in the shortest possible time. Apart from a redefinition of the SI second, this also facilitates tests of physics beyond the Standard Model 6, 7, 8, 9 and opens up the field of relativistic geodesy 10, 11, 12. ![]() In recent years, atomic clocks based on optical transitions 1 have achieved unprecedented levels in accuracy and stability as frequency references 2, 3, 4, 5. In contrast, clocks based on smaller, non-scalable ensembles, such as ion clocks, can already benefit from squeezed states with current clock lasers. Even with a future improvement of the laser performance by one order of magnitude the critical atom number still remains below 100,000. We find that for usual cyclic Ramsey interrogation of single atomic ensembles with dead time, even with the current most stable lasers spin squeezing can only improve the clock stability for ensembles below a critical atom number of about one thousand in an optical Sr lattice clock. Our analytic predictions are in good agreement with numerical simulations of the closed servo-loop. Based on an analytic model of the closed servo-loop of an optical atomic clock, we report here quantitative predictions on the optimal clock stability for a given dead time and laser noise. Here, we investigate the benefits of spin squeezed states for clocks operated with typical Brownian frequency noise-limited laser sources. While further improvements to the stability have been envisioned by using entangled atoms, squeezing the quantum mechanical projection noise, evaluating the overall gain must incorporate essential features of an atomic clock. Optical atomic clocks are a driving force for precision measurements due to the high accuracy and stability demonstrated in recent years. ![]()
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